We still don't know what the exact result is, so we take the exponent of both sides of the equation above with some change on the right side. As its name suggests, it is the most frequently used form of logarithm. It is used, for example, in our decibel calculator. Logarithm tables that aimed at easing computation in the olden times usually presented common logarithms, too.

To demonstrate how useful it was in pre-calculator times, let's assume that you need to compute the product of 5.89 × 4.73 without any electronic device. You could do it by merely multiplying things out on paper; however, it would take a bit of time. Instead, you can use the logarithm rule with log tables and get a relatively good approximation of the result. A percentage is also a way to express the relation between two numbers as a fraction of 100. In other words, the percentage tells us how one number relates to another. If we know that number A is 25% of number B, we know that A to B is like 25 is to 100, or, after one more transformation, like 1 to 4, i.e., A is four times smaller than B. This is what the percentage calculator teaches; what is a percentage and how to find a percentage of two numbers. So what is percentage good for? As we wrote earlier, a percentage is a way to express a ratio. Say you are taking a graded exam. If we told you that you got 123 points, it really would not tell you anything. 123 out of what? Now, if we told you that you got 82%, this figure is more understandable information. Even if we told you, you got 123 out of 150; it's harder to feel how well you did. A week earlier, there was another exam, and you scored 195 of 250, or 78%. While it's hard to compare 128 of 150 to 195 of 250, it's easy to tell that an 82% score is better than 78%. Isn't the percent sign helpful? After all, it's the percentage that counts!You can choose various numbers as the base for logarithms; however, two particular bases are used so often that mathematicians have given unique names to them, the natural logarithm and the common logarithm. One practical way to understand the function of the natural logarithm is to put in the context of compound interest. That is the interest that is calculated on both the principal and the accumulated interest. Percentage is one of many ways to express a dimensionless relation between two numbers (the other methods being ratios and fractions). Percentages are very popular since they can describe situations that involve large numbers (e.g., estimating chances for winning the lottery), averages (e.g., determining the final grade of your course), as well as very small ones (like the volumetric proportion of NO₂ in the air, also frequently expressed by PPM — parts per million). lg ( 5.89 ) ≅ 0.7701153 \text{lg}(5.89) ≅ 0.7701153 lg ( 5.89 ) ≅ 0.7701153 and lg ( 4.73 ) ≅ 0.674861 \text{lg}(4.73) ≅ 0.674861 lg ( 4.73 ) ≅ 0.674861

You may notice that even though the frequency of compounding reaches an unusually high number, the value of (1 + r/m)ᵐ (which is the multiplier of your initial deposit) doesn't increase very much. Instead, it becomes somewhat stable: it's approaching a unique value already mentioned above, e ≈ 2.718281. The term percent is often attributed to Latin per centum, which means by a hundred. Actually, it is wrong. We got the term from Italian per cento — for a hundred. The percent sign % evolved by the gradual contraction of those words over centuries. Eventually, cento has taken the shape of two circles separated by a horizontal line, from which the modern % symbol is derived. The history of mathematical symbols is sometimes astonishing. We encourage you to take a look at the origin of the square root symbol! Change in percentage points (pp): The difference between two percentage values. If one value is 10 % and the other is 30 %, the change is 20 percentage points (20 pp). This situation is when percentage points come in handy. We use percentage points when we want to talk about a change from one percentage to another. A change from 10% to 12% is two percentage points (or 20 percent). The percentage tells you how number A relates to number B. A real-world example could be: there are two girls in a group of five children. What's the percentage of girls? In other words, we want to know what's the ratio of girls to all children. It's 2 out of 5, or 2/5. We call the first number (2) a numerator and the second number (5) a denominator because this is a fraction. To calculate the percentage, multiply this fraction by 100 and add a percent sign. 100 × numerator / denominator = percentage. In our example, it's 100 × 2/5 = 100 × 0.4 = 40. Forty percent of the group are girls. That's the entire procedure of converting between decimal fractions and percentages.times 4.73 ≅ 10 Other than being helpful with learning percentages and fractions, this tool is useful in many different situations. You can find percentages in almost every aspect of your life! Anyone who has ever been to the shopping mall has surely seen dozens of signs with a large percentage symbol saying " discount!". And this is only one of many other examples of percentages. They frequently appear, e.g., in finance, where we use them to find an amount of income tax or sales tax, or in health to express what is your body fat. lg ( 5.89 × 4.73 ) = lg ( 5.89 ) + lg ( 4.73 ) ≅ 0.770115 + 0.6748611 \text{lg}(5.89 \times 4.73) =\text{lg}(5.89) + \text{lg}(4.73) ≅ 0.770115 + 0.6748611 lg ( 5.89 × 4.73 ) = lg ( 5.89 ) + lg ( 4.73 ) ≅ 0.770115 + 0.6748611